Consider a square chessboard with ~N \times N~ cells and ~M~ queens on the chessboard (Note: there are no other chess pieces besides the queens).
A queen can move vertically, horizontally or diagonally. As an example, consider the square chessboard with ~6\times6~ cells with one queen (denoted by the
♕ notation) in Figure 1 below. The cells
that can be reached by the queen are marked with the
◯ notation. There are ~16~ cells cannot be reached by the queen.
Your task is to calculate the number of cells that are NOT reachable by any queens.
The first line contains two integers, ~N~ and ~M~. ~(1 \le N \le 100, 1 \le M \le 10)~. Following are ~M~ lines. Each line contains two integers ~x~ and ~y~, representing the location of a queen, i.e., the queen is at ~x~th row and ~y~th column ~(1 \le x, y \le N)~.
The number of cells that are not reachable by any queens.
Sample Input 1
6 1 4 3
Output for Sample Input 1
Sample Input 2
6 2 4 3 6 4
Output for Sample Input 2
Figure 1 and Figure 2 correspond to Sample 1 and Sample 2, respectively.